Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking soda, and salt.
In a large bowl, cream together the vegan butter, granulated sugar, and brown sugar until light and fluffy. Add the flax egg and vanilla extract, and mix well.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
Fold in the crushed candy canes.
Using a cookie scoop or spoon, form balls of dough and flatten slightly into discs. Place a chocolate sandwich cookie on top of each disc of dough and wrap the dough around the cookie, sealing the edges.
Place the cookies on the prepared baking sheet and bake for 12-14 minutes.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.